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arXiv · 1308.4275

Efficient estimation of eigenvalue counts in an interval

Edoardo Di Napoli·Eric Polizzi·Yousef Saad
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Abstract

Estimating the number of eigenvalues located in a given interval of a large sparse Hermitian matrix is an important problem in certain applications and it is a prerequisite of eigensolvers based on a divide-and-conquer paradigm. Often an exact count is not necessary and methods based on stochastic estimates can be utilized to yield rough approximations. This paper examines a number of techniques tailored to this specific task. It reviews standard approaches and explores new ones based on polynomial and rational approximation filtering combined with a stochastic procedure.

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Edoardo Di Napoli, Eric Polizzi, Yousef Saad. 2013-08-20. Efficient estimation of eigenvalue counts in an interval. https://arxiv.org/abs/1308.4275

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